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Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities

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Abstract

A classical predator-prey model is considered in this paper with reference to the case of periodically varying parameters. Six elementary seasonality mechanisms are identified and analysed in detail by means of a continuation technique producing complete bifurcation diagrams. The results show that each elementary mechanism can give rise to multiple attractors and that catastrophic transitions can occur when suitable parameters are slightly changed. Moreover, the two classical routes to chaos, namely, torus destruction and cascade of period doublings, are numerically detected. Since in the case of constant parameters the model cannot have multiple attractors, catastrophes and chaos, the results support the conjecture that seasons can very easily give rise to complex populations dynamics.

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Authors and Affiliations

  1. Politecnico di Milano, CIRITA, 20133, Milano, Italy

    Sergio Rinaldi

  2. Centro Teoria dei Sistemi, CNR, Politecnico di Milano, 20133, Milano, Italy

    Simona Muratori

  3. Research Computing Centre, Russian Academy of Sciences, 142292, Pushchino, Moscow Region, Russia

    Yuri Kuznetsov

Authors
  1. Sergio Rinaldi
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  2. Simona Muratori
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  3. Yuri Kuznetsov
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Rinaldi, S., Muratori, S. & Kuznetsov, Y. Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities. Bltn Mathcal Biology 55, 15–35 (1993). https://doi.org/10.1007/BF02460293

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  • DOI: https://doi.org/10.1007/BF02460293

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